There are 3 campground in Horseshoe Meadow, Cottonwood Lakes, Cottonwood Pass and Equestrian. Cottonwood Pass is the largest and, to my mind, Cottonwood Lakes is the best...we always stay there no matter which trailhead we utilize.
I cannot picture either the Equestrian or the Pass filling up on a Friday night. I've think we've only been shut out once at Lakes.
Sweat other things, not this.